How do you evaluate $\sin \left( \arcsin 0.3 \right)$ ?
(a) Using trigonometric angle identities
(b) Using linear formulas
(c) a and b both
(d) none of the above

Hint: In this problem we are trying to evaluate $\sin \left( \arcsin 0.3 \right)$. We will start by considering the value of $\arcsin (0.3)=x$. Then by analyzing the properties of trigonometric inverse functions we can conclude that the value we will get would be 0.3.

Complete step by step solution:
According to this problem, we are to evaluate the value of $\sin \left( \arcsin 0.3 \right)$.
Now, The arcsin function is the inverse of the sine function. It returns the angle whose sine is a given number. For every trigonometry function, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. So the inverse of sin is arcsin. When we see "arcsin A", we understand it as "the angle whose sin is A".
Let us consider that,
$\arcsin (0.3)=x$ which implies that, $\sin x=0.3$ .
Now,
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Identity inequalities which are true for every value occurring on both sides of an equation. Geometrically, these identities involve certain functions of one or more angles. There are various distinct identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle.
So,$\sin \left( \arcsin 0.3 \right)$gives us the result of sinx.
We are getting $\sin x$giving us our needed value.
This gives us a value of 0.3.

So, the correct answer is “Option a”.

Note: Inverse trigonometric functions like $\arcsin (0.3)$ are simply defined as the inverse functions of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant functions. They are also termed as arcus functions, anti trigonometric functions or cyclometric functions. These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios. Inverse trigonometric functions are also called “Arc Functions” since, for a given value of trigonometric functions, they produce the length of arc needed to obtain that particular value. The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle. These six important functions are used to find the angle measure in the right triangle when two sides of the triangle measures are known.